7thth Grade Math
Module 1: Ratios and Proportional Relationships
Math Parent Letter
This document is created to give parents and students a better
Focus Area Topic D:
Ratios of Scale Drawings
Example Problem and Answer
Use the following figures to answer the questions below:
understanding of the math concepts found in Eureka Math (© 2013
Common Core, Inc.) that is also posted as the Engage New York
material which is taught in the classroom. Module 1 of Eureka Math
(Engage New York) builds on ratios, rates, and unit rates to formally
define proportional relationships and the constant of proportionality.
Focus Area Topic D:
Ratios of Scale Drawings
Words to Know:
Scale Drawing - a reduced or enlarged two-dimensional
drawing of an original two-dimensional drawing.
One-to-One Correspondence - Each point in one
figure corresponds to one and only one point in the
second figure.
Scale Drawing - A drawing in which all lengths
between points or figures in the drawing are reduced or
enlarged proportional to the lengths in the actual picture.
A constant of proportionality exists between
corresponding lengths of the two images.
Reduction - The lengths in the scale drawing are smaller
than those in the actual object or picture.
Enlargement/Magnification: The lengths in the scale
drawing are larger than those in the actual object or
picture.
Scale Factor: corresponds to the unit rate and the
constant of proportionality. It can be calculated from
the ratio of any length in the scale drawing to its
corresponding length in the actual picture.
Question: Is the New Picture a reduction or enlargement
from the Actual Picture?
Answer: It is a reduction because the New Picture is
smaller than the Actual Picture.
Question: Which point on the New Picture corresponds
to point A on the Actual Picture?
Answer: Point G; Corresponding points match from one
picture to another.
Task: Complete the chart for corresponding
measurements.
Question: Does the constant of proportionality exist? If
so, how do you know?
Answer: Yes, because there is a constant value ( ) to get
from each length to its corresponding length. (See work and
values below).
Focus Area Topic D:
Focus Area Topic D:
Ratios of Scale Drawings
Ratios of Scale Drawings
Scale factors are utilized in building models, homes, etc.
Example Problem and Solution
Students learn the term scale factor and recognize the
constant of proportionality. With the scale factor, students
make scale drawings of pictures and diagrams.
On the Ferris’ house blueprints, the master bathroom measures
inches by
inches. If the scale factor for the blueprint is
.
Question:
What are the actual dimensions of the master bathroom?
Answer with solution:
or 4 feet per inch
Question:
Given the figures below, find the scale factor.
Therefore:
feet
And
8
feet
The master bathroom is 18 feet by 33 feet
Answer & Explanation:
The scale factor is 2. Create a ratio of corresponding
lengths of the scale drawing to the original drawing.
The scale factor is
Question:
Reverse the process. If given the dimensions of the
original drawing, compute the dimensions of the scale
drawing if the scale factor is .
Actual Length
12 inches
15 inches
because the ratio
from the scale
drawing to the
actual drawing is
.
Scale Length
inches
inches
Steps to check for proportionality for scale drawing
and original object/picture:
1) Measure lengths of scale drawing. Record on table.
2) Measure corresponding lengths on actual
picture/drawing. Record on table.
3) Check for constant of proportionality.
The Actual Area = 9 units x 6 units = 54 square units
The Scale Drawing Area = 2 units x 3 units
= 6 square units
Ratio of Scale Drawing Area to Actual Area:
Notice: ( )
… the square (multiplying it times
itself) of the scale factor is the ratio of the areas of the
scale drawing and the actual picture.
Scale Drawing Process:
1. Measure lengths and widths carefully with a ruler or tape measure.
Record in an organized table.
2. Calculate the scale drawing lengths, widths and areas using what was
learned in previous lessons.
3. Calculate the actual areas.
4. Begin by drawing the perimeter, windows and doorways.
5.Continue to draw the pieces of furniture making note of placement
of objects (distance from nearest wall).